The present invention relates to a method and an apparatus for detecting a sound source.
Recently, requirements for reducing noise from a vehicle have become severe in view of environment concerns, and thus various studies for reducing noise have been performed for a tire as well as a vehicle body itself.
In a conventional method for measuring tire noise, a sound pressure level of the noise is measured by means of one microphone arranged apart by a constant distance from the tire rotating on a test table. However, in this known method, it is impossible to specify that portion of the tire which produces noise and provide useful data for reducing the noise level.
In this connection, in order to obtain the sound pressure of the noise together with its direction, a study about acoustic intensity has been developed. Hereinafter, acoustic intensity will be explained.
In an acoustic field, a sound emitted, from the sound source can be described in the term of a total power and an emitting direction thereof, and thus an arbitrary point in the acoustic field to be investigated can be expressed only by these two information. The power of the sound source can be expressed by a sum of energy fluxes passing through a closed-surface surrounding it. The acoustic intensity is described by the energy fluxes passing through a unit surface perpendicular to a sound propagating direction within a unit time and the unit thereof is expressed by [Watt/m.sup.2 ]. Therefore, if it is assumed that the total power of the sound source is W and acoustic intensity on the closed-surface A is I, the following equation is derived. EQU W=.intg..intg..sub.A I.multidot.dA (1)
An instantaneous value I(r) of the acoustic intensity I at a point r is described by a product between the sound pressure (scalar amount) and an acoustic velocity (vector amount), and normally expressed by the folowing equation with taking an average time into account, ##EQU1## where E is an expected value, P(r, t) is the sound pressure at the point r and V(r, t) is the acoustic velocity at the point r.
In case of measuring only the sound pressure representing the scalar amount, since the sound pressure does not include the component of the sound propagating direction, it is very difficult to accurately grasp an acoustic output of the sound generated from the sound source to be observed due to the influence of noise reflected by the surrounding portions and generated from other portions, and also difficult to detect accurately the position of the sound source.
Contrary to this, in case of measuring the noise by the acoustic intensity representing the vector, since the strength and the direction of the transmitting sound can be detected, it is possible to measure accurately the acoustic output of the sound source to be observed without being affected by the sound generated from the other portions. Moreover, it is possible to derive accurately the position of the sound source by measuring a distribution of the sound strength.
As mentioned above, the acoustic intensity is characterized in that it is expressed by the product between the sound pressure (scalar amount) and the acoustic velocity (vector amount). Here, the sound pressure can be measured directly by a microphone, but it is very difficult to measure the acoustic velocity. Therefore, as shown in FIG. 1, two microphones 1-1 and 1-2 are arranged apart by a constant distance .DELTA.r, and the acoustic intensity is derived by calculating respective outputs of these microphones 1-1 and 1-2. That is to say, in FIG. 1, if it is assumed that the outputs representing the sound pressure of the microphones 1-1 and 1-2 are P.sub.1 (t) and P.sub.2 (t), respectively, the sound pressure P(t) at the middle point between two microphones is approximated by the following equation. EQU P(t)=1/2[P.sub.2 (t)+P.sub.1 (t)] (3)
Moreover, an inclination of the sound pressure in an arrow direction in FIG. 1 is also approximated as follows; ##EQU2## Therefore, the acoustic velocity can be approximated in the following manner; ##EQU3## where .rho. is the density of air.
In this manner, the acoustic intensity is obtained by calculating the sound pressure and the acoustic velocity derived from the equations (3) and (5), respectively. This calculation method is a so-called acoustic wattmeter and has been studied for a long time. Further, since recently it becomes easy to effect an examination in a frequency field by using a fast Fourier transform (FFT), a method for deriving the acoustic intensity by using a cross spectrum has been developed.
Hereinafter, the method for deriving the acoustic intensity by using the cross spectrum will be explained.
At first, the Fourier transforms of the sound pressure P(r) and the acoustic velocity V(r) at the point r are described respectively as follows; ##EQU4## where j=.sqroot.-1. Since the sum of the acoustic intensity in the time field is equal to that in the frequency field, the following relation must be satisfied; ##EQU5## where V*(r, f) denotes the complex conjugate of V(r, f).
Here, a density function J of the acoustic intensity is described as follows. EQU J(r, f)=E[P(r, f)V*(r, f)] (9)
Since the integration of the density function J in the frequency field is equal to the acoustic intensity I, the following equation is derived. ##EQU6##
If the abovementioned method for deriving the acoustic intensity by using the cross spectrum is applied to that by using two microphones 1-1 and 1-2, the Fourier transforms of the sound pressure and the acoustic velocity respectively shown in equations (3) and (5) can be expressed by the following equations, respectively. ##EQU7## Therefore, the density function J of the acoustic intensity can be rewritten in the following manner. ##EQU8## In the equation (12), a term j2.pi.f in a denominator appears as a result of the integration in the frequency field.
In equation (13), since the following equation is satisfied; EQU P.sub.2 *P.sub.1 -P.sub.1 *P.sub.2 =2jIm(P.sub.1 P.sub.2 *), (14)
the density function J can be rewritten into the following equation. ##EQU9## In this case, since a term E[.vertline.P.sub.2 .vertline..sup.2 -.vertline.P.sub.1 .vertline..sup.2 ] denotes a real even function with respect to the frequency and a term ##EQU10## is an odd function, an imaginary part of the density function J becomes the odd function and thus becomes zero after effecting the integration shown in the equation (10).
Therefore, the acoustic intensity I is described as follows; ##EQU11## where ##EQU12## In this equation, a term P.sub.1 P.sub.2 * denotes a density of cross spectrum and a term E[Im(P.sub.1 P.sub.2 *)] is an imaginary part of the cross spectrum. Therefore, the acoustic intensity I can be derived easily by a two-channel FFT. The distance .DELTA.r between two microphones 1-1 and 1-2 is a set a value corresponding to a sound frequency range to be measured, i.e. a smaller value in the high frequency range and a larger value in the low frequency range.
Hereinbefore, the explanation was made to the acoustic intensity and the method for calculating the acoustic intensity by using the cross spectrums detected by the two microphones. As to an apparatus for detecting the sound source by using the acoustic intensity derived from the cross spectrum, for example, an apparatus for detecting the sound source of a car engine has been well known. In this apparatus, a number of probes each having three microphones spaced apart from each other are secured to a frame surrounding the engine to be observed, and in each probe outputs of two microphones are selected among them corresponding to the frequency range of the sound to be measured. Then, these probes are electrically scanned and the acoustic intensities with respect to various frequencies are calculated at each of the probe arranging positions.
In the abovementioned apparatus for detecting the sound source, since it is necessary to arrange many probes for measuring the acoustic intensities with respect to various frequencies at many points, the apparatus is made large in size and expensive in cost. Moreover, since the measuring point i.e. the probe arranging position is limited so much, it is not possible to set a measuring interval etc. at will. Further, it becomes very troublesome work to adjust many microphones to have identical characteristics.